Mathematical models for predicting P excretions play a key role in evaluating P use efficiency and monitoring the environmental impact of dairy cows. However, the majority of extant models require feed intake as predictor variable, which is not routinely available at farm level. The objectives of the study were to (1) explore factors explaining heterogeneity in P output; (2) develop a set of empirical models for predicting P output in feces (Pf), manure (PMa), and milk (Pm, all in g/cow per day) with and without dry matter intake (DMI) using literature data; and (3) evaluate new and extant P models using an independent data set. Random effect meta-regression analyses were conducted using 190 Pf, 97 PMa, and 118 Pm or milk P concentration (PMilkC) treatment means from 38 studies. Dietary nutrient composition, milk yield and composition, and days in milk were used as potential covariates to the models with and without DMI. Dietary phosphorus intake (Pi) was the major determinant of Pf and PMa. Milk yield negatively affected Pi partitioning to Pf or PMa. In the absence of DMI, milk yield, body weight, and dietary P content became the major determinants of Pf and PMa. Milk P concentration (PMilkC) was heterogeneous across the treatment groups, with a mean of 0.92 g/kg of milk. Milk yield, days in milk, and dietary Ca-to-ash ratio were negatively correlated with PMilkC and explained 42% of the heterogeneity. The new models predicted Pf and PMa with root mean square prediction error as a percentage of observed mean (RMSPE%) of 18.3 and 19.2%, respectively, using DMI when evaluated with an independent data set. Some of the extant models also predicted Pf and PMa well (RMSPE%=19.3 to 20.0%) using DMI. The new models without DMI as a variable predicted Pf and PMa with RMSPE% of 22.3 and 19.6%, respectively, which can be used in monitoring P excretions at farm level. When evaluated with an independent data set, the new model and extant models based on milk protein content predicted PMilkC with RMSPE% of 12.7 to 19.6%. Although models using P intake information gave better predictions, P output from lactating dairy cows can also be predicted well without intake using milk yield, milk protein content, body weight, and dietary P, Ca, and total ash contents.

The objective of the current study was to develop Bayesian simultaneous equation models for modelling energy intake and partitioning in growing pigs. A key feature of the Bayesian approach is that parameters are assigned prior distributions, which may reflect the current state of nature. In the models, rates of metabolizable energy (ME) intake, protein deposition (PD) and lipid deposition (LD) were treated as dependent variables accounting for residuals being correlated. Two complementary equation systems were used to model ME intake (MEI), PD and LD. Informative priors were developed, reflecting current knowledge about metabolic scaling and partial efficiencies of PD and LD rates, whereas flat non-informative priors were used for the reminder of the parameters. The experimental data analysed originate from a balance and respiration trial with 17 cross-bred pigs of three genders (barrows, boars and gilts) selected on the basis of similar birth weight. The pigs were fed four diets based on barley, wheat and soybean meal supplemented with crystalline amino acids to meet or exceed Danish nutrient requirement standards. Nutrient balances and gas exchanges were measured at c. 25, 75, 120 and 150 kg body weight (BW) using metabolic cages and open circuit respiration chambers. A total of 56 measurements were performed. The sensitivity analysis showed that only the maintenance component was sensitive to the prior specification, and hence the maintenance estimate of 0·91 MJ ME/kg0·60 per day (0·95 credible interval (CrI): 0·78-1·09) should be interpreted with caution. It was shown that boars' ability to deposit protein was superior to that of barrows and gilts, as these had an estimated maximum PD (PDmax) of 250 g/day (0·95 CrI: 237-263), whereas the barrows and gilts had a PDmax of 210 g/day (0·95 CrI: 198-220). Furthermore, boars reached PDmax at 109 kg BW (0·95 CrI: 93·6-130), whereas barrows and gilts maximized PD at 81·7 kg BW (0·95 CrI: 75·6-89·5). At 25 kg BW, the boars partitioned on average 5-6% more of the ME above maintenance into PD than barrows and gilts, and this was progressively increased to 10-11% more than barrows and gilts at 150 kg BW. The Bayesian modelling framework can be used to further refine the analysis of data from metabolic studies in growing pigs. © Cambridge University Press 2012.

Food production including dairy has been associated with environmental impacts and resource use that has been steadily improving when adjusted per unit of product. The objective of this study was to conduct a cradle-to-farm gate environmental impact analysis and resource inventory of the California dairy production system to estimate the change in greenhouse gas emissions and water and land use over the 50-yr period between 1964 and 2014. Using a life cycle assessment according to international standards and the Food and Agriculture Organization of the United Nations guidelines, we analyzed contributions from dairy production in California to global environmental change. Production of 1 kg of energy- and protein-corrected milk (ECM) in California emitted 1.12 to 1.16 kg of CO₂ equivalents (CO₂e) in 2014 compared with 2.11 kg of CO₂e in 1964, a reduction of 45.0 to 46.9% over the last 50 yr, depending on the model used. Greater reductions in enteric methane intensity (i.e., methane production per kilogram of ECM) were observed (reduction of 54.1 to 55.7%) compared with manure GHG (reduction of 8.73 to 11.9%) in 2014 compared with 1964. This was mainly because manure management in the state relies on lagoons for storage, which has a greater methane conversion factor than solid manure storage. Water use intensity was reduced by 88.1 to 89.9%, with water reductions of 88.7 to 90.5% in crop production, 55.3 to 59.2% in housing and milking, and 52.4 to 54% in free water intake. Improved crop genetics and management have contributed to large efficiencies in water utilization. Land requirements for crop production were reduced by 89.4 to 89.7% in 2014 compared with 1964. This was mainly due to dramatic increases in crop yields in the last 50 yr. The increases in milk production per cow through genetic improvements and better nutrition and animal care have contributed to reductions in greenhouse gas emissions and land and water usage when calculated per unit of production (intensity) basis.

Nutrient loading and air emissions from swine operations raise environmental concerns. The objective of the study was to describe and evaluate a mathematical model (Davis Swine Model) of nutrient partitioning and predict manure excretion and composition on a daily basis. State variables of the model were AA, fatty acids, and a central pool of metabolites that supplied substrate for lipid synthesis and oxidation. The model traced the fate of ingested nutrients and water through digestion and intermediary metabolism into body protein, fat, water, and ash, where body protein and fat represented the body constituent pools. It was assumed that fluxes of metabolites follow saturation kinetics, depending on metabolite concentrations. The main inputs to the model were diet nutrient composition, feed intake, water-to-feed ratio, and initial BW. First, the model was challenged with nutrient partitioning data and then with excretion data. The data had 48 different feeding regimes with contrasting energy and lysine intakes at 2 different stages of growth. The overall observed and predicted mean were 109 and 112 g/d for protein deposition and 132 and 136 g/d for lipid deposition respectively, suggesting minor mean bias. Root mean square prediction error (RMSPE) was used in evaluation of the model for its predictive power. The overall RMSPE was 2.2 and 4.1 g/d for protein and lipid deposition, respectively. The excretion database used for evaluation of the model was constructed from 150 digestibility trials using growing-finishing pig diets that had a wide range of nutrient chemical composition. Nutrient and water excretion were quantified using the principle of mass conservation. The average daily observed and predicted manure production was 3.79 and 3.99 kg/d, respectively, with a RMSPE of 0.49 kg/d. There was a good agreement between observed and predicted mean fecal N output (9.9 and 9.8 g/d, respectively). Similarly, the overall observed and predicted mean urine N output was 21.7 and 21.3 g/d, respectively, suggesting minor mean bias. The RMSPE was 1.9 and 4.1 g/d for fecal and urinary N, respectively. Evaluation of the model showed that the model predicts manure excretion and N content well and can be used to assess environmental mitigation options from swine operations.

Experiments designed to investigate the effect of dietary nutrient concentrations on the growth and development of pullets are relatively long term and expensive to conduct. As the cost of research increases, mathematical models become valuable tools to answer research and development questions. Modeling growth curves allows nutritionists and poultry researchers to predict dynamic or daily nutrient needs more adequately than using fixed requirements. The potential and validity of a specially reparameterized monomolecular model to partition nutrient intakes between requirements for maintenance and growth was previously demonstrated in relation to ruminants, pigs, chickens, turkeys, and broiler breeder pullets. In the current study, the model was evaluated for its ability to estimate ME and CP requirements for maintenance and growth in egg-type pullets. On the basis of the results of this study, along with those previously reported for chickens, turkeys, and broiler breeder pullets, this model is advantageous because it can predict the magnitude and direction of responses of growing poultry to dietary ME and CP intakes without requiring initial assumptions. The model also has the advantage of biological interpretability of the parameter estimates. One of the main consequences of this interpretability is that the results from several experiments can be pooled to obtain the best estimates of the response coefficients. ©2012 Poultry Science Association, Inc.

Manure nitrogen (N) from cattle production facilities can lead to negative environmental effects, such as contribution to greenhouse gas emissions, leaching and runoff to aqueous ecosystems leading to eutrophication, and acid rain. To mitigate these effects and to improve the efficiency of N use, accurate prediction of N excretion and secretions are required. A genetic algorithm was implemented to select models to predict fecal, urinary, and total manure N excretions, and milk N secretions from 3 classes of animals: lactating dairy cows, heifers and dry cows, and steers. Two tiers of model classes were developed for each category of animals based on model input requirements. A total of 6 models for heifers and dry cows and steers and an additional 2 models for lactating dairy cattle were developed. Evaluation of the models using K-fold cross validation based on all data and using the most recent 6 yr of data showed better prediction for total manure N and fecal N compared with urinary N excretion, which was the most variable response in the database. Compared with extant models from the literature, the models developed in this study resulted in a significant improvement in prediction error for fecal and urinary N excretions from lactating cows. For total manure production by lactating cows, extant and new models were comparable in their prediction ability. Both proposed and extant models performed better than the prediction methods used by the US Environmental Protection Agency for the national inventory of greenhouse gases. Therefore, the proposed models are recommended for use in estimation of manure N from various classes of animals.

Goat genotype may alter the net energy and protein requirements for maintenance (NEm and NPm, respectively) and weight gain (NEg and NPg).This study was designed to investigate and quantify the effect of goat type on NEm, NPm, NEg and NPg, and quantify the net requirements for energy and protein for dairy, meat and indigenous growing male goats. For that, comparative slaughter studies were gathered and a meta-analytical approach was used. Two distinct databases were organized: one composed of 233 individual records from 11 studies of meat (n = 81), dairy (n = 97) and indigenous (n = 55) growing male goats weighing from 4.50 to 51.0 kg, to depict NEm and NPm; and another database composed of 239 individual records from nine studies of meat (n = 87), dairy (n = 97) and indigenous (n = 55) growing male goats weighing from 4.30 to 51.0 kg, to depict NEg and NPg. Our findings showed that NEm of meat goats was 8.5% greater (336 ± 10.8 kJ/kg0.75 of empty BW; EBW) than dairy and indigenous goats (310 ± 8.20 kJ/kg0.75 EBW; P < 0.05). Whereas, NPm was not affected by goat type (1.92 ± 0.239 g/kg EBW; P = 0.91). The NPg was 185.1 ± 1.82 g/kg of EBW gain for goats weighing 5 kg BW and 192.5 ± 4.33 g/kg of EBW gain for goats weighing 45 kg BW, and thus did not change across goat type (P = 0.12). On the other hand, NEg increased from 7.29 ± 0.191 to 11.9 ± 0.386 MJ/kg of EBW in male dairy goats, and from 7.32 ± 0.144 to 15.7 ± 0.537 MJ/kg of EBW in meat and indigenous growing male goats weighing between 5 and 45 kg BW. When body protein was used as a predictor in the allometric equation instead of EBW seeking to account for the degree of maturity, goat type differences disappeared; however, this predictor showed a high variation among individuals. In conclusion, energy and protein requirements for gain in distinct goat types reflect on body composition differences. Future research should focus on better understanding the maturity degree and its consequences in the energy requirement of growing male goats and better depict the goat type effect on it, as well as on the efficiency of utilization.

Mathematical models that predict water intake by drinking, also known as free water intake (FWI), are useful in understanding water supply needed by animals on dairy farms. The majority of extant mathematical models for predicting FWI of dairy cows have been developed with data sets representing similar experimental conditions, not evaluated with modern cows, and often require dry matter intake (DMI) data, which may not be routinely available. The objectives of the study were to (1) develop a set of new empirical models for predicting FWI of lactating and dry cows with and without DMI using literature data, and (2) evaluate the new and the extant models using an independent set of FWI measurements made on modern cows. Random effect meta-regression analyses were conducted using 72 and 188 FWI treatment means with and without dietary electrolyte and daily mean ambient temperature (TMP) records, respectively, for lactating cows, and 19 FWI treatment means for dry cows. Milk yield, DMI, body weight, days in milk, dietary macro-nutrient contents, an aggregate milliequivalent concentration of dietary sodium and potassium (NaK), and TMP were used as potential covariates to the models. A model having positive relationships of DMI, dietary dry matter (DM%), and CP (CP%) contents, NaK, and TMP explained 76% of variability in FWI treatment means of lactating cows. When challenged on an independent data set (n=261), the model more accurately predicted FWI [root mean square prediction error as a percentage of average observed value (RMSPE%)=14.4%] compared with a model developed without NaK and TMP (RMSPE%=17.3%), and all extant models (RMSPE%≥15.7%). A model without DMI included positive relationships of milk yield, DM%, NaK, TMP, and days in milk, and explained 63% of variability in the FWI treatment means and performed well (RMSPE%=17.9%), when challenged on the independent data. New models for dry cows included positive relationships of DM% and TMP along with DMI or body weight. The new models with and without DMI explained 75 and 54% of the variability in FWI treatment means of dry cows and had RMSPE% of 12.8 and 15.2%, respectively, when evaluated with the literature data. The study offers a set of empirical models that can assist in determining drinking water needs of dairy farms.

Air and nutrient emissions from swine operations raise environmental concerns. During the reproduction phase, sows consume and excrete large quantities of nutrients. The objective of this study was to develop a mathematical model to describe energy and nutrient partitioning and predict manure excretion and composition and methane emissions on a daily basis. The model was structured to contain gestation and lactation modules, which can be run separately or sequentially, with outputs from the gestation module used as inputs to the lactation module. In the gestating module, energy and protein requirements for maintenance, and fetal and maternal growth were described. In the lactating module, a factorial approach was used to estimate requirements for maintenance, milk production, and maternal growth. The priority for nutrient partitioning was assumed to be in the order of maintenance, milk production, and maternal growth with body tissue losses constrained within biological limits. Global sensitivity analysis showed that nonlinearity in the parameters was small. The model outputs considered were the total protein and fat deposition, average urinary and fecal N excretion, average methane emission, manure carbon excretion, and manure production. The model was evaluated using independent data sets from the literature using root mean square prediction error (RMSPE) and concordance correlation coefficients. The gestation module predicted body fat gain better than body protein gain, which was related to predictions of body fat and protein loss from the lactation model. Nitrogen intake, urine N, fecal N, and milk N were predicted with RMSPE as percentage of observed mean of 9.7, 17.9, 10.0, and 7.7%, respectively. The model provided a framework, but more refinements and improvements in accuracy of prediction (particularly urine N) are required before the model can be used to assess environmental mitigation options from sow operations.